How exactly does Blender perform a simple deformation?
By following the file history I can find that it was originally developed in the soc-2008-jaguarandi branch. The original documentation for it is here but I don't see any explanation of the algorithm used and there are no comments on papers used.

If you could find a copy of the gsoc application it may have a description of the algorithm.

It's also possible that you could contact jaguarandi who may still remember how it works.